Term Algebra - Herbrand Base

The signature σ of a language is a triple consisting of the alphabet of constants O, the function symbols F, and the predicates P. The Herbrand base of a signature σ consists of all ground atoms of σ: of all formulas of the form R(t1, …, tn), where t1, …, tn are terms containing no variables (i.e. elements of the Herbrand universe) and R is an n-ary relation symbol (i.e. predicate). In the case of logic with equality, it also contains all equations of the form t1=t2, where t1 and t2 contain no variables.

Read more about this topic:  Term Algebra

Famous quotes containing the word base:

    “Adolescence is a time when children are supposed to move away from parents who are holding firm and protective behind them. When the parents disconnect, the children have no base to move away from or return to. They aren’t ready to face the world alone. With divorce, adolescents feel abandoned, and they are outraged at that abandonment. They are angry at both parents for letting them down. Often they feel that their parents broke the rules and so now they can too.”
    —Mary Pipher (20th century)